A conductor AB of length L carrying a current I', is placed perpendicular to a long straight conductor XY carrying a current I as shown in Fig. The forces on AB has magnitude

Options

A. `(mu_0I'I)/(2pi)log2`
B. `(mu_0I'I)/(2pi)log3`
C. `(3mu_0I'I)/(2pi)log3/2`
D. `(2mu_0I'I)/(3pi)`

Answer

B

Explanation

(b) Consider an element of length dx on AB, at a distance x from
XY. Force on the element,
`dF=(mu_0I//2pix)I'dx`
Total force on AB,
`F=int_(L//2)^(3L//2) (mu_0II')/(2pix)`dx of `F=(mu_0II')/(2pi)log3`